& BRIEFLY NOTED: For 2021-12-16 Th: IN JANUARY I am, once again, appropriating the intellectual property of the brilliant Melissa Dell <https://dell-research-harvard.github.io>, and trying to teach my own version of her course Economics 1342: The History of Economic Growth <https://dell-research-harvard.github.io/teaching/econ1342>.. Here is what I am thinking of doing for the first lecture...
> The square-root is a compromise. Is it the right compromise? We can argue about that. What would you suggest?
I think income is something of a trap concept. The Micawber principle -- Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds nought and six, result misery -- applies.
So I think the useful measure is the amount and proportion of agency in the population.
You can have a high income, with high expenses and no resilience -- get sick, you're dead; miss a deadline, you're dead, etc. -- and have effectively no agency; you do what you must to survive. You are not as much better off than someone with less cash flow doing what they must to survive as the difference in the magnitude of the cash flow implies.
People want to be billionaires today because billionaires today have got effectively unbounded agency; if it can be done, they can do it. Most people today are aware that their agency is decreasing, and was and would have been even without covid.
The patterns of degree -- how far could someone in 13th century England go on a pilgrimage, and how often? -- and distribution -- persons of what degree could go on pilgrimages? -- are very likely tougher to pull out of history than income proxies, but I think that's where the interesting pattern lies.
I also think it's obvious that the post-1870 surge is spending from capital, not income, and has a high likelihood of reducing everyone's access to agency for the foreseeable future.
In the few existing hunter/gatherer groups it is often a 'women gather-men hunt' pattern. This suggests that if this pattern held in neolithic times, women invented agriculture.
I've been fascinated by growth models since high school when I learned about exponential growth. Since then, I've noticed increasing interest in models in which growth increases more quickly than proportionally to quantity. I'm sure I followed one link from this site to a paper arguing that urban growth has to account for the increased interaction in the development of new ideas.
That gets me to something called "coalition growth" which gets mentioned surprisingly rarely given its effectiveness in modeling human population growth. The idea is that the growth rate is best modeled not exponentially but as an increasing function of the population. That is, large groups of people reproduce more quickly than those in smaller groups. (I have a link below to discussion of coalition growth which includes a reference to a 1960 paper in Science which I should probably read.) This fits in with the idea of economic growth exceeding mere growth.
P.S. There are probably other inflection points hidden in history: the cooked food revolution, the stone tool revolution, the primary agricultural revolution, the secondary products revolution and so on.
"The square-root is a compromise. Is it the right compromise? We can argue about that. What would you suggest?"
It is often the case that when you need a convex function, the square root has the right stylized behaviour but analysis supports the logarithm. I don't have such an analysis, but again, often network effects scale in log(N).
"Nevertheless, the large cumulative magnitude of technological progress in the past: as much from -6000 to 1870 as from 1870-2010."
I interpret this to mean that 1 / 0.51 = 19.6, the 2010 value. But this fact does not "jump out at me from this table"; I have to perform the computation. On the other hand, if H were defined to be log, then the -6000 value would be -5.95 and the 2010 value would be 5.95 and your observation would be self-evident. And since 1 / 0.51 = 19.6 is a geometric comparison, it seems all the more natural to use logarithms.
> The square-root is a compromise. Is it the right compromise? We can argue about that. What would you suggest?
I think income is something of a trap concept. The Micawber principle -- Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds nought and six, result misery -- applies.
So I think the useful measure is the amount and proportion of agency in the population.
You can have a high income, with high expenses and no resilience -- get sick, you're dead; miss a deadline, you're dead, etc. -- and have effectively no agency; you do what you must to survive. You are not as much better off than someone with less cash flow doing what they must to survive as the difference in the magnitude of the cash flow implies.
People want to be billionaires today because billionaires today have got effectively unbounded agency; if it can be done, they can do it. Most people today are aware that their agency is decreasing, and was and would have been even without covid.
The patterns of degree -- how far could someone in 13th century England go on a pilgrimage, and how often? -- and distribution -- persons of what degree could go on pilgrimages? -- are very likely tougher to pull out of history than income proxies, but I think that's where the interesting pattern lies.
I also think it's obvious that the post-1870 surge is spending from capital, not income, and has a high likelihood of reducing everyone's access to agency for the foreseeable future.
In the few existing hunter/gatherer groups it is often a 'women gather-men hunt' pattern. This suggests that if this pattern held in neolithic times, women invented agriculture.
I've been fascinated by growth models since high school when I learned about exponential growth. Since then, I've noticed increasing interest in models in which growth increases more quickly than proportionally to quantity. I'm sure I followed one link from this site to a paper arguing that urban growth has to account for the increased interaction in the development of new ideas.
That gets me to something called "coalition growth" which gets mentioned surprisingly rarely given its effectiveness in modeling human population growth. The idea is that the growth rate is best modeled not exponentially but as an increasing function of the population. That is, large groups of people reproduce more quickly than those in smaller groups. (I have a link below to discussion of coalition growth which includes a reference to a 1960 paper in Science which I should probably read.) This fits in with the idea of economic growth exceeding mere growth.
https://services.math.duke.edu/education/postcalc/growth/growth3_1.html
P.S. There are probably other inflection points hidden in history: the cooked food revolution, the stone tool revolution, the primary agricultural revolution, the secondary products revolution and so on.
"The square-root is a compromise. Is it the right compromise? We can argue about that. What would you suggest?"
It is often the case that when you need a convex function, the square root has the right stylized behaviour but analysis supports the logarithm. I don't have such an analysis, but again, often network effects scale in log(N).
"Nevertheless, the large cumulative magnitude of technological progress in the past: as much from -6000 to 1870 as from 1870-2010."
I interpret this to mean that 1 / 0.51 = 19.6, the 2010 value. But this fact does not "jump out at me from this table"; I have to perform the computation. On the other hand, if H were defined to be log, then the -6000 value would be -5.95 and the 2010 value would be 5.95 and your observation would be self-evident. And since 1 / 0.51 = 19.6 is a geometric comparison, it seems all the more natural to use logarithms.
Touche